Activities to help students conceptualize the multiplication of a fraction with a whole number.

Problem Solving

Start by having the student, using drawings, manipulatives, etc, develop their own methods of finding solutions to the following problems. This will help them to conceptualize the meaning of multiplying fractions.

• Answer in fractions. Your neighbor is going on a trip. He would like you to let his dog outside morning, noon and evening. He offers to pay you ¼ of a dollar each time. How much money would you earn in 3 days? In 6 days?
• If you drink ½ cup of water four times a day, how many cups of water would you drink in 4 days?
• Jill filled 5 glasses with 2/5 of a liter of juice in each glass. How much juice did she use?

Manipulatives

Have the students further develop and strengthen their conceptual understanding by using a variety of different representations. This will help them not only scaffold their understanding, but will help them to transfer their learning for use in other situations.

Fraction pies (or bars) (physical- fraction bar chart) or (virtual manipulatives -nlvm.com pattern blocks)

• Ask the students to put out a 1/3 piece and find the answer to 3 x 1/3 If we make 1/3 three times bigger. Repeat for 4 x 1/5, 3/17, 5 x 1/3, 3 x 1/3, etc.
• Ask the student to put out 2/3 pieces and then to find the answer to 4 x 2/3. Repeat for 2x ¾, 5 x 4/5, 4 x 5/6, etc.

Number lines (pictorial number lines or rulers)

• Explain that to the students that they have a jumping frog (walker, runner, etc). Each time it moves it goes ¼ of an inch. Using the number line show how far the frog will get in 5 moves or if the frog went five times further. Repeat for a variety of numbers.

Pictorial models

• Give the student a page of small boxes or circles
• Ask them to demonstrate, using the images 2/3 of 2 or 2/3x2 (They would split each of the two boxes into 1/3’s and color in 2 of the 1/3s of each box.
• Repeat for a variety of problems.

Teach the students that when multiplying you can replace the x with the word "of"

• Begin with whole groups. If you have 3 groups of 2 cards how many cards would you have?
• Use a manipulative or draw the pictures of two groups of 3.
• Write the symbolic sentence: 3 of 2 is 6 and 3 x 2 = 6
• Repeat with different problems until students are comfortable with writing sentences both ways
• Ask students to demonstrate, calculate, and compare answer to the following: 3 x 1/3 (three groups of 1/3) and 1/3 of 3 (1/3 of 3)
• Repeat with other numbers until students transfer the idea that the two perspectives are equal.

Help students to realize that when multiplying a whole number by a fraction less than one, the product will be less than the whole number factor.

• Read with the students Multiplying Menace; The Revenge of Rumpelstiltskin by Pam Calvert ISBN13-978-1-57091-890-2. In this story there is a wicked wizard that takes over the kingdom by multiplying objects with the touch of his staff. The hero of the story learn to say a fraction when using the staff to decrease all of the objects.

  • Multiplying Menace: The Revenge Of Rumpelstiltskin (A Math Adventure)

Practice

• Multiply Fractions Lines/Circles

http://www.visualfractions.com/multiply.htm
Gives a visual picture of multiplying a fraction with a whole number

• Fraction mystery Picture

http://www.dositey.com/2008/math/mistery2.html
Students multiply fractions times whole numbers to uncover a picture.